Eddies

Eddies#

This section covers the detection, tracking, and analysis of mesoscale ocean eddies using shoot. Eddies are rotating coherent structures that play a crucial role in ocean circulation and transport.

What are Ocean Eddies?#

Ocean eddies are circular currents of water that rotate around a center:

Cyclonic eddies:

  • Rotate counterclockwise in Northern Hemisphere

  • Clockwise in Southern Hemisphere

  • Associated with upwelling and cooler water

  • Negative sea surface height anomaly

  • Positive LNAM signature

Anticyclonic eddies:

  • Rotate clockwise in Northern Hemisphere

  • Counterclockwise in Southern Hemisphere

  • Associated with downwelling and warmer water

  • Positive sea surface height anomaly

  • Negative LNAM signature

Characteristics#

Spatial scales:

  • Diameter: 50-500 km (mesoscale)

  • Typical: 100-200 km at mid-latitudes

  • Scale with Rossby radius of deformation

Temporal scales:

  • Lifetime: Weeks to months

  • Can persist for over a year

  • Rotation period: Days to weeks

Physical properties:

  • Swirl velocity: 0.1-1 m/s

  • Rossby number: 0.1-0.5

  • Vertical extent: 100-1000+ m

Importance#

Eddies are important because they:

  • Transport heat, salt, and nutrients

  • Influence biological productivity

  • Impact fisheries and marine ecosystems

  • Affect acoustic propagation

  • Contribute to ocean mixing

  • Play a role in climate

Detection in shoot#

shoot detects eddies using the LNAM method (Local Normalized Angular Momentum):

  1. Compute LNAM field from velocity components (u, v)

  2. Apply Okubo-Weiss filter to identify vortex-dominated regions

  3. Find local extrema as potential eddy centers

  4. Extract SSH contours around each center

  5. Identify maximum velocity contour as eddy boundary

  6. Compute properties (radius, intensity, shape)

  7. Apply quality filters (size, ellipticity, validity)

The method is detailed in Eddy Detection.

Key Parameters#

window_center (km):

  • Scale for LNAM computation

  • Typically 1-2 × Rossby radius

  • ~50 km for mid-latitude altimetry

window_fit (km):

  • Search domain for SSH contours

  • Typically 5-10 × Rossby radius

  • ~120 km for mid-latitude altimetry

min_radius (km):

  • Minimum eddy size to retain

  • Often set to Rossby radius

  • ~15 km for mid-latitudes

ellipse_error (fraction):

  • Maximum deviation from perfect ellipse

  • 0.05 (5%) for clean satellite data

  • 0.10 (10%) for noisy model output

Tracking in shoot#

shoot tracks eddies through time using the Chelton et al. (2011) algorithm:

  1. Detect eddies at each time step

  2. Compute cost matrix based on:

    • Spatial distance between centers

    • Rossby number similarity

    • Radius similarity

    • Type matching (cyclone/anticyclone)

  3. Find optimal matching using Hungarian algorithm

  4. Update existing tracks or create new ones

  5. Handle births and deaths of eddies

The tracking system is detailed in Eddy Tracking.

Key Parameters#

max_distance (km):

  • Maximum search radius for matching

  • Based on typical advection distance

  • ~50 km for daily data

Dt (days):

  • Actual time interval between detections

  • Affects cost function weighting

Tc (days):

  • Characteristic time scale

  • Typically 10-20 days for mesoscale

Quick Example#

Basic Detection#

from shoot.eddies.eddies2d import Eddies2D
import xarray as xr

# Load data
ds = xr.open_dataset("velocity_field.nc")

# Detect eddies
eddies = Eddies2D.detect_eddies(
    ds.u,              # Zonal velocity
    ds.v,              # Meridional velocity
    window_center=50,  # Detection window (km)
    window_fit=120,    # Fitting window (km)
    ssh=ds.ssh,        # Optional SSH field
    min_radius=15      # Minimum radius (km)
)

# Results
print(f"Detected {len(eddies.eddies)} eddies")
for eddy in eddies.eddies:
    print(f"  {eddy.eddy_type} at ({eddy.lon:.1f}, {eddy.lat:.1f})")
    print(f"    Radius: {eddy.radius:.1f} km")

Basic Tracking#

# Detect at multiple times
eddies_list = []
for t in range(len(ds.time)):
    eddies_t = Eddies2D.detect_eddies(
        ds.u.isel(time=t),
        ds.v.isel(time=t),
        50, 120, min_radius=15
    )
    eddies_list.append(eddies_t)

# Track (see tracking guide for full implementation)
# tracks = track_eddies(eddies_list, max_distance=50)

Advanced Topics#

3D Detection#

Detect eddies across multiple depth levels and associate vertically:

from shoot.eddies.eddies3d import EddiesByDepth

# 3D velocity field
eddies_3d = EddiesByDepth.detect_eddies_3d(
    ds.u,              # 3D zonal velocity
    ds.v,              # 3D meridional velocity
    window_center=50,
    window_fit=120,
    max_distance=10    # Max vertical shift (km)
)

# Access by depth
for depth in eddies_3d.eddies3d:
    print(f"Depth {depth}: {len(eddies_3d.eddies3d[depth].eddies)} eddies")

Profile Association#

Link in-situ observations with detected eddies:

from shoot.profiles.profiles import Profiles

# Load Argo profiles
profiles = Profiles.from_ds(ds, root_path="./argo_data")

# Associate with eddies
profiles.associate(eddies, nlag=2)  # ±2 days

# Profiles inside vs outside
inside = profiles.ds.where(profiles.ds.eddy_pos >= 0, drop=True)
outside = profiles.ds.where(profiles.ds.eddy_pos == -1, drop=True)

See Working with Profiles for details.

Acoustic Analysis#

Assess how eddies affect sound propagation:

from shoot.hydrology import Anomaly
from shoot.acoustic import AcousEddy

# Create anomaly from eddy and profiles
anomaly = Anomaly(eddy, profiles.ds, nlag=2)

if anomaly.is_valid():
    # Analyze acoustic impact
    acous = AcousEddy(anomaly)
    impact = acous.acoustic_impact

    print(f"Acoustic impact: {impact:.3f}")
    print(f"Surface duct: {acous.ecs_inside:.1f} m inside")
    print(f"              {acous.ecs_outside:.1f} m outside")

Data Sources#

Satellite Altimetry#

Best for surface eddy detection:

  • Products: DUACS, AVISO, CMEMS

  • Resolution: 1/4° (~25 km)

  • Temporal: Daily

  • Variables: SSH, geostrophic velocities

  • Coverage: Global oceans

Ocean Models#

Provide 3D structure:

  • Models: CROCO, NEMO, MOM

  • Resolution: 1/12° to 1/36° (~2-8 km)

  • Temporal: Hourly to daily outputs

  • Variables: U, V, SSH, T, S at multiple depths

  • Coverage: Regional or global

Reanalysis#

Combines models and observations:

  • Products: GLORYS, ORAS

  • Resolution: 1/12° (~8 km)

  • Temporal: Daily

  • Variables: 3D fields (U, V, T, S)

  • Coverage: Global, multi-decadal

Best Practices#

Parameter Selection#

  1. Start with standard values based on latitude

  2. Adjust based on data resolution

  3. Validate with known eddies if available

  4. Check sensitivity to parameters

  5. Document chosen values

Quality Control#

  1. Visually inspect detected eddies

  2. Check size distribution is reasonable

  3. Verify tracking produces smooth trajectories

  4. Remove spurious short-lived features

  5. Validate against independent data

Performance#

For large datasets:

  • Process subregions separately

  • Use parallel detection (with caution)

  • Save intermediate results

  • Consider coarser temporal sampling

Common Issues#

No Eddies Detected#

Possible causes:

  • Insufficient velocity magnitude

  • Grid resolution too coarse

  • Parameters too restrictive

  • Data quality issues

Solutions:

  • Check velocity field statistics

  • Reduce min_radius

  • Adjust window sizes

  • Verify data integrity

Too Many False Positives#

Possible causes:

  • Noisy data

  • Parameters too permissive

  • Insufficient quality filtering

Solutions:

  • Increase min_radius

  • Decrease ellipse_error

  • Add coastal masking

  • Filter by duration in tracking

Tracking Failures#

Possible causes:

  • max_distance too small

  • Detection inconsistency

  • Large time gaps

  • Rapid eddy evolution

Solutions:

  • Increase search distance

  • Improve detection parameters

  • Interpolate missing times

  • Adjust cost function weights

Further Reading#

Comprehensive guides:
Algorithm details:

  • Eddies - Mathematical description

  • algos.track - Tracking algorithm

Related topics:
Scientific references:

  • Chelton et al. (2011) - Tracking algorithm

  • Faghmous et al. (2015) - Detection methods

  • Nencioli et al. (2010) - Eddy characterization